Neuroscientists often describe neural activity as a representation of something, or claim to have found evidence for a neural representation. But what do these statements mean? The reasons to call some neural activity a representation and the assumptions that come with this term are not generally made clear from its common uses in neuroscience. Representation is a central concept in philosophy of mind, with a rich history going back to the ancient period. In order to clarify its usage in neuroscience, here we advance a link between the connotations of this term across these disciplines. We draw on a broad range of discourse in philosophy to distinguish three key aspects of representation: correspondence, functional role, and teleology. We argue that each of these aspects are implied by the explanatory role the term plays in neuroscience. However, evidence related to all three aspects is rarely presented or discussed in the course of individual studies that aim to identify representations. Overlooking the significance of all three aspects hinders communication in neuroscience, as it obscures the limitations of experimental paradigms and conceals gaps in our understanding of the phenomena of primary interest. Working from this three-part view, we discuss how to move toward clearer communication about representations in the brain.